ACTSC 446/846 Winter 2013
Mathematical Models for Finance
Assignment 1
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Due: Thursday Feb 7th, 2013 in class. Hard copy please. No electronic version.
To earn the full credit of

ACTSC 446/846 - Problem Set 2
1. Assume a one-period model securities market model with two assets S1 and S2 . The prices
at time 0 and at time 1 are respectively given by:
1.25 10
S(0) = [ 1 , 5 ], S(1, ) = 1.25 6 .
1.25
3
(a) What is the risk-free rate

ACTSC 446/846 - Problem Set 2
1. Assume a one-period model securities market model with two assets S1 and S2 . The prices
at time 0 and at time 1 are respectively given by:
1.25 10
S(0) = [ 1 , 5 ], S(1, ) = 1.25 6 .
1.25 3
(a) What is the risk-free rate

Actsc 446/846 - Tutorial 9
1. Using the formulas on the nal exam formula sheet, nd the price of the following
derivatives under the B-S framework:
(a) a derivative which pays at time T , the maximum of ST and a xed amount G.
(b) a derivative which pays at

ACTSC 446/846 - Assignment 2
Due on February 27th, 2014 by the end of class
1. Consider an asset with a current price of $50 and a volatility of 10% each year. Suppose the
assets price is modelled using a binomial tree with monthly time steps. The continu

ACTSC 446/846 - Assignment 1 Solution
1. For each of the following strategies, draw a graph of the payo:
(a) A bull spread: Buy a call with a strike of 9 and sell a call with a strike of 11
(b) A straddle: Buy a call and a put, each with a strike of 9
Sol

ACTSC 446/846 - Assignment 3 Solution
1. Suppose W = cfw_Wt , t 0 is a standard BM process. Find the dynamics of the following
processes.
(a) Zt =
t
0 g(u)dWu ,
where g is an adapted stochastic process.
Solution:
This is simply an It process in integral f